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Can someone explain is common sense terms how circles,squares, and Triangles apply to Aikido Techniques? Maybe someone can
recommend a good book I can read that will clarify the concept for me.
I've read " The dynamic sphere" but that book is to technical and it loses me in some chapters.

We have, however, proof that Ueshiba learned Yagyu Shinkage-ryu with some degree of depth. This proof lies in the sword method of Hikitsuchi Michio. Hikitsuchi taught three sword forms, called Sho (matsu — pine), Chiku (take — bamboo), and Bai (ume — plum). According to Meik Skoss, who trained under Hikitsuchi, "Sho" embodies Irimi — the triangle; "Chiku" embodies Tenkan — the circle: and "Bai" embodies Osae — the square. Fascinatingly, these three kumitachi forms are modifications of forms from Yagyu Shinkage-ryu: "Sho" is Kaboku, #4 from Kuka no Tachi; "Chiku" is Settetsu, #2 from Sangakuen no Tachi; and "Bai" is Ozume, #7 from Kuka no Tachi. In essence, then, not only did Ueshiba learn a good deal of the Yagyu Shinkage-ryu curriculum, he abstracted out three different forms as a: the embodiment of what were, to him, the three fundamental principals of his art, and b. creating a curriculum, using these forms as "containers," specifically tailored to Hikitsuchi Michio.

I like that idea.
Myself, I prefer the ellipse instead of the circle, when it comes to aikido - and all budo. For example, I like to think of the relation between tori and uke as the two focal points of an ellipse - each person's center being one of them.
There are no circles in the universe - only ellipses.

I tend to think of "circle power" as movement that favors the relative.
I prefer to think of "spiral power" which of course is movement that has the relative, but the absolute is the main focus. Circles in aikido tend to lack the necessary "intention" to my way of thinking.

Triangle, Circle, Square
Three Principles
Re: Sankaku/Maru/Shikaku—Triangle/Circle/Square…the Kaiso (O’Sensei) could study Triange /Circle/ Square at Tsubaki Grand Shrine- the Main Shrine of SarutahikonoOkami who is Ancestor of all Earthly Kami, Guardian Kami of Aikido and the Kami of progressing positively in harmony with the ceaseless movements of Great Nature.

May I share this information from Ise-noKuni Ichi-no-Miya, Sarutahiko Daihongu Tsubaki O Kami Yashiro?
In his book Kami no Michi, Rev. Dr. Yukitaka Yamamoto, the 96th generation High Priest (Guji) wrote:

"The Principle of 'Sanmi-Sangen' explains the mystery of life. Sanmi-Sangen means the three elements that constitute the basis of all forms of existence. These basic symbols both explain the meaning of and guide the destiny of human life. We can see Sanmi-Sangen operate at many levels."
So, we as Aikido practitioners can see that in Shinto cosmology, the relates to "Gogyo Gogen." Following the blueprints created by the Amatsu (heavenly) Kami, the Kunitsu (earthly) Kami made the "Ki" of trees, fire, soil, gold and water. Gas turns to be a liquid and a solid , while a solid turns to a liquid and gas . This transformation (Kami Musubi - a Fire & Water Knot [Musubi = Tie where existence and non-existence are unified]), is holographically mirrored in the aiki waza of Ueshiba O'Sensei.
Archetypically, all Aiki waza moves from Triangle to Circle to Square….each waza has a beginning, a middle and an end and offers a real chance to experience the live mystery of entraining with Kannagara-no-Ugoki (ceaseless movement of divine nature) progressing as follows:
• triangle -
Sankaku-no-irimi: Sankakutai - the hanmi prior to deai (initial physical contact) . Establishment of angle and radius of entry (triangle) is power of harmonization. Zenshin.
• circle -
En-no-irimi: The spiralic movements (omote and ura) of aiki technique . Tsushin.
• square -
Chokusen-no-irimi: The explosive power (shunpatsu rokyu) of a kokyu nage like extension and the expanding echo (zanshin) or osae waza (pinning technique) . Zanshin.

Further- if our waza is lacking one of these elements we are unlikely to receive the Harae (the purification) of the technique….we must generate KI, resolve completely to return to zero (to emptiness) to create the space for Kiyome (the invigoration)…we must have a fresh mind for each technique (whether we train quickly or slowly----speed and intensity are different issues) to enter completely into the current moment.
In the doctrine of O'Harahi (Great Purification) as explained by Yamamoto Guji the means mission. Mission means a share of the work that helps realize the ideal of O'Kami. The is Life. Life stands between mission and the flow of fate. This is vertical and horizontal musubi. The is fate. Fate is the result of all things based on the actions of the past - the flow of fate is horizontal musubi.
In his book The Kototama Commentary Concerning the O Harahi published (in Japanese) by Tsubaki O Kami Yashiro, Yamamoto Guji further explains, "Those who are aware of mission (future) and boil their blood to do their best in their lives (present) are able to alter the currents ([and purify] the past) of fate."
This is the mission established by the vertical tie and unmediated connection to the breath and heartbeat of Kami.

******************************************************
Shinto and Human Life from Tsubaki Grand Shrine of America website:

The principle of sanmi-sangen explains the mystery of life. Sanmi-sangen means the three elements that constitute the basis of all forms of existence. these basic symbols guide the destiny of human life. We can see sanmi-sangen operate at many levels, and it is the interaction of theselevels that can product forces that will work for the benefit and well-being of those who follow their lead - people whose behavior and thinking are characterized by the way of the Kami.
At the level of the Kami, Amaterasu O Kami, the deity of the Sun who lives in Takamanohara, the Utopia of brightness, is principal aamong the three important parts of the cosmological dimension of existence. The sun is the source of life, of growth and of creativity. Without its heat, power and energy, life could not exist. Thus, the universe is totally dependent upon the primal force of the sun.
Tsukuyomi-no-mikoto, the Kami of the moon, is the guardian of night, the time of silent growth and development, the necessary complement to the day. The moon symbolizes these in its cycle: the new moon, the half moon, the full moon. the moon waxes and wanes as does life in the process of growth. Shinrabansho, or everything in nature, depends on the growth time of the moon, just as everything depends on the light and power of the sun.
Susanoo-no-mikoto, the deity of the stars, was given authority over the vastness of the ocean, unabara. Without water, the earth cannot live. The ebb and flow of the life is under higher governance and that governance is the destiny of man whose place is creation is described in Japanese by the expression banbutsu-no-reicho, the lord of everything under the sun.
These three, the deities of the sun, moon, and stars, are called the san-ko, the three lights and their existence is fundamental for all forms of life in the universe.
When spring comes all the flowers begin to bloom towards summer, insects begin to appear, birds sing and human beings begin to move in response to their Ki, power or energy. Spring is naturally the time of romance when love blossoms, people marry, and the soul of man enters the female spirit and body and new life comes into being. The flow of all things is from the gaseous state to the liquid and then to the solid. Ki generates feeling which turn into solid. Ki generates feelings which turn tot he liquid forms of love and then the solid forms of birth and reproduction. Thus nature flows eternally and is as we know it. In Shinto symbolism, the triangle symbolizes the gaseous, the circle symbolizes the liquid, and the square smbolizes the solid.
This symbolism encompasses all aspects of cosmic and earthly existence, showing how life is built and governed and how its destiny should flow. The Buddhist expression for this is rinne, transmigration of the sould, samsara in Sanskrit.
To have meaning life must have balance between mission and destiny. We must think quite deeply about these. Mission has quite a specific meaning. If two people produce a child, this does not mean the presence of mission. The child who is not the product of mission and destiny is the child who will perhaps end up abandoned, whose conception and birth were not surrounded by the protective structures that the union of life, mission and destiny can produce. If these are present, however, that life can be nurtured properly and grow into the fulfillment of its own destiny. In addition that life, in union with another, will continue its natural flow, projecting life into the future, united in mission and destiny, according to Kannagara. So the generations are born and life ceaselessly flows.

Mission Life Destiny
Sangen in Daily Ife
Sangen, the rule of three main factors, works at the level of everyday life and at the level of human destiny. In every shrine, offerings to the Kami on sambo (offering stand), include certain items apart from sake, vegetables and fruits - namely salt, rice and water. the offerings, called shinsen, presents the basis of life.
For Japanese, life has been based on rice and rice requires water for growth. The ancient Japanese knew the power of water to make rice grow. The Shinto terms minaoshi (forward) and kikinaoshi (obedient) contain the secrets of how that power was harnessed.
Water in a bottle can be passive and obedient, but uncontained, water can be a torrent tearing down trees and destroying walls. Water can fertilize and stimulate growth. If people could live like creative water, they would find life less tiring. The flexibility of water is a great lesson.
Allied to the role of water and of equal importance is time and timing. The shrine's nenchu gyoji - schedule of rituals - covers the entire year, and each stage in life. Shinto is very time conscious. What is the most important aspect of human existence? Some might answer, "life," but I would say, "time," because life is very much a sequence of events.
These events follow in order, and that order cannot be changed. Cherry blossoms will not appear in December. No matter how much you may wish to see them, you have to wait until spring. That is their time. Time is perhaps why Japanese are so time conscious. Time you cannot see, but it is time that enables us to understand the processes of nature. This is turn encourages us to feel thankful. Thankfulness is important in Shinto because it expresses our repectful dependence on the powers that determine the flow of our lives.
Discontentment will lead only to frustration. If there is one word or one sentiment that should govern our way of thinking and that expresses the true spirit of Kanngara, it is the Japanese term Kansha - simply giving things to the powers that make people their care and that assist them in reaching the true greatness of spirit they were born to know.
Thank you
Rev. Koichi Barrish
Senior Shinto Priest of
Tsubaki Grand Shrine of Americawww.TsubakiShrine.orghttp://groups.yahoo.com/group/Tsubakiko/kannushi@TsubakiShrine.org

"The body should be triangular, the mind circular. The triangle represents the generation of energy and is the most stable physical posture. The circle symbolizes serenity and perfection, the source of unlimited techniques. The square stands for solidity, the basis of applied control."
--Morihei Ueshiba

I can't quite remember where I obtained this quote but it makes sense to me!

Shareef Muhammad

"In order to change our condition, we must first change our way of thinking...it is actually thought that changes us.

"The body should be triangular, the mind circular. The triangle represents the generation of energy and is the most stable physical posture. The circle symbolizes serenity and perfection, the source of unlimited techniques. The square stands for solidity, the basis of applied control."
--Morihei Ueshiba

I can't quite remember where I obtained this quote but it makes sense to me!

This is a quote that has been around for a while, and I think it's a good place to start.

For me the Square, Circle, and Triangle flow into each other - Nage starts within the solidity of the Square, aware of the eight directions that are possible for attack - then moves into a Triangle entry and posture for proper position and angle, and then finally allows the Circle - or actually (Spiraling) Sphere - to manifest, which is the basis for proper execution of all Aikido Technique, or in my mind, the Release.

I think there is a fair amount instruction tied up in the triangle, circle, square concept.
For new students, I will sometimes use the concept to get them to develop a process:
Stand in a balanced solid foundation
Focus intent on your partner
Move circularly in harmony with the technique (i.e. no harsh edges)

Imaizumi sensei describes the three shapes in terms of training progression. The square for basic training that can look almost like wrestling. The triangle for the phase in which you technique becomes sharp and decisive. The circle for the return to softness.

Imaizumi sensei describes the three shapes in terms of training progression. The square for basic training that can look almost like wrestling. The triangle for the phase in which you technique becomes sharp and decisive. The circle for the return to softness.

some list members made "off-list "contact with deep interest in the information from the Jinja Shinto......so may I share just a bit more:

TAKAAMAHARA= meaning is 1) the Universe 2) the High Plain of Heaven...it is the place of origin..the place of AMENOMINAKANUSHINOOKAMI [1st Kami] and the 15 pillars or 15 Kami of seven generations that are the source of creation...the place of Amatsukami Takamaahara is represented by a triangle.

TAKAMANOHARA= meaning is 1) the Solar System 2) the place where Amatsu Kami created the blueprint for the physical world.....the place where the supreme Kami ritual of eternal emission of divine light is performed Takamanohara is represented by a circle.

GENKAI-the Real World= IzanaginoOkami and IzanaminoOkami created the solar system as the two pillars and then descended to Onogorojima (self condensing ball/Earth) to continue their mission of creation...then the Earthly Kami continue the mission of divine creation based on truth and principle. This real world is led by Earthly Kami led by SARUTABIKO-NO-MIKOTO ( Ancestor Kami of Aikido, also known as SARUTAHIKONOOKAMI, DOUKOUJIN, OKITAMANOOKAMI, DOUSO JIN and DOUROUKUJIN etc) the Real World is represented as a square.